56. A bankrupt's available property can be sold for $19,780, which will pay 62 cents on every dollar he owes. How much does he owe? 57. A loaf of bread weighing 2 pounds, when flour is worth $9.80 per barrel, is sold for 10 cents. What should it bring when flour is worth $7.84? 58. Divide 0.75 of 17g by of 0.035. 59. An army of 7844 men has 490,250 pounds of beef. If for every man 1 pounds daily be allowed, in how many days will the beef be consumed? 60. A seedsman bought 37 bushels of lawn grass-seed for $226. He sold 25 bushels at a profit of $13 per bushel. For what price per bushel must he sell the remainder to make his whole gain $73? 61. The cost of 50 gallons of molasses is $25. By leakage of it is lost; 20 gallons are sold at 62 cents. At what rate must the remainder be sold to gain $5 on the whole? 62. For of a yard of broadcloth at $6 per yard, 1 yards of cassimere and 50 cents in money were given in exchange. What was the price per yard of the cassimere? 63. A owns of a ship and cargo worth $25,748, B † of the remainder, Cof the amount belonging to A and B, and D owns what is still left. Required the amount of D's share. 64. A farmer gives to his eldest son 1 of a farm, and the remainder to his daughter. The difference between their shares is 780 acres. How many acres does the daughter receive? 65. f 1200 pounds can be carried 36 miles for $14, how many pounds can be carried 24 miles for $14? 66. If 21 acres of land cost $500, what will 460 acres cost? 67. Four and four-sevenths tons of cannel coal cost $64. Required the cost of 135 tons. 68. Of a certain estate is pasture, land suitable for cultivation, and the remainder, woodland, is 50 acres. How many acres in the estate? 69. If 1.4 bushels of walnuts cost $1.50, find the value of 7 bushels. 70. If a man breathes 17 times a minute, and takes in at each breath of a quart of air, how many quarts of air does he need in 1 hour? 71. If the crop of potatoes from an acre is on the average 255 bushels, but the potato beetle destroys of the crop, how many bushels will 34 acres produce? 72. If a miller takes for toll, and a bushel of wheat produces 40 pounds of flour, how many bushels must be carried to the mill to obtain 196 pounds of flour? 73. An expressman carried 100 vases, on the condition that he was to receive of a dollar for every one he carried without breaking, and pay 14 dollars for every one he broke. He received 16 dollars. many did he break? HINT. How The expressman loses $9 on the lot, and he loses $1 on each vase broken. 74. A man who rows 4 miles an hour in still water takes 1 hours to row 4 miles up a river. How many minutes will it take him to row 4 miles down the river? HINT. The man rows 44 miles in 1 hours. Hence the current sets him back ‡ of a mile in 13 = § hours, or ÷ § = } of a mile in 1 hour. In rowing down the river he rows 4 miles an hour, and the current carries him of a mile an hour, CHAPTER IX. COMPOUND QUANTITIES. 142. A quantity expressed with reference to a single unit is called a simple quantity; but a quantity expressed with reference to different units is called a compound quantity. Thus, 20 pounds is a simple quantity, but 20 pounds 4 ounces is a compound quantity. 143. The process of changing the unit in which a quantity is expressed, without changing the value of the quantity, is called, reduction. 144. If the change be from a higher denomination to a lower, it is called reduction descending; if from a lower to a higher, it is called reduction ascending. Thus, 1 yard = 36 inches is an example of reduction descending; and 24 inches 2 feet is an example of reduction ascending. measuring the height of horses) = 4 in.; a palm 9 in.; a cubit a link = = 3 in.; a span 18 in.; a military pace 22 ft.; a chain 4 rds. ; = To chain; a furlong = mi.; a knot (used in navigation) = 6086 ft.; a nautical league = 3 knots; a fathom (used in measuring == depths at sea) = 6 ft.; a cable length = 120 fathoms. Ex. 98. (Oral.) 1. How many inches in 1 yd.? in yd.? in 4 yd.? 2. How many yards in 180 in. ? in 48 in.? in 45 in.? 3. How many yards in 3 rds.? in 4 rds.? in 5 rds.? 4. How many feet in 2 yds.? in 2 rds.? in 2 rds. 2 yds.? 5. How many rods in 33 ft.? How many yards in 33 ft.? 6. In mi. how many rods? yards? feet? 7. How many rods in 0.4 of a mile? in 0.3? in 0.7? 8. What part of a mile are 160 rds.? 80 rds.? 40 rds.? 9. What part of a foot are 4 in.? 3 in.? 6 in.? 8 in.? 10. What part of a yard are 2 ft.? 1 ft. 6 in.? 2 ft. 6 in.? REDUCTION DESCENDING. 146. Change 10 mi. 40 rds. to feet. 10 mi. 40 rds. 320 3200 40 3240 16 1620 19440 3240 53460 10 x 320 rds. 3200 rds., to which the 40 rds. are added. Again, 3240 × 163 ft. = 53,460 ft. The multiplicand and multiplier are interchanged in the operation. Reduce to feet: 1. 3 mi. 5 yds. 2 ft. Ex. 99. Reduce to inches: 4. 18 mi. 252 rds. 2 yds. 147. Change 53,463 ft. to a compound quantity. There are 16 ft., or 33 half-feet, in a rod; so the 53,463 ft. are changed to half-feet, and the half-feet to rods, by dividing by 33. The remainder is 6 half-feet = 3 ft. 3240 rds. are changed to miles by dividing by 320, the number of rods in a mile. The remainder is 40 rds. The yd. of the 4 ♦ and the result, 1 ft. 6 5 mi... 303 rds. yds. should be reduced to lower denominations, in., added to the 2 ft. 5 in. Thus, mi. rds. yds. ft. in. 5 303 4 2 5 1 6 5 303 5 0 11 5 mi. 303 rds. 5 yds. 0 ft. 11 in. Ans. |